Monte Carlo investigation of the mixed spin Ising model with four-spin interaction and next-nearest neighbor couplings

•We investigate a two-dimensional mixed spin Ising model with four-spin interaction J4 and next-nearest neighbor coupling J′.•In the absence of the next-nearest neighbor interactions, the system does not present a tricritical behavior.•The influence of the next-nearest neighbor interaction depends on the positive and negative value of J′.•For J′ < 0, the system exhibits, at zero-temperature, a phase transition at a finite critical value (J4)C.•For J′ > 0 and J4 = −4 the system keeps the coexistence of two ground states up to a J′-dependent finite temperature.

A Monte Carlo method is used to investigate the phase diagram of the ferromagnetic two-dimensional mixed spin-1 and spin-1/2 Ising model with four-spin interaction J4 and next-nearest couplings J′. In the absence of this latter interaction, the system does not present any evidence for the tricritical point, whereas such behavior was suggested by finite cluster approximation. In the presence of the next-nearest neighbor interaction, the phase diagram is qualitatively and quantitatively different from that obtained with J′ = 0. It undergoes two kinds of behaviors according to the negative and positive value of J′. In particular, for J4/J2 = −4 the system keeps the coexistence of the two ground states up to a J′-dependent finite temperature. In addition to the phase diagrams, the thermal dependence of the magnetizations have also been examined. Some characteristic features have been found which depend on the strengths of the interactions J4 and J′.